package org.rasterfun.utils;

/**
 * Simplex noise in 2D, 3D and 4D.
 *
 * Based on "Simplex noise demystified" paper by Stefan Gustavson.
 */
public class SimplexNoise
{
    private static int grad3[][] = { { 1, 1, 0 }, { -1, 1, 0 }, { 1, -1, 0 }, { -1, -1, 0 },
                                     { 1, 0, 1 }, { -1, 0, 1 }, { 1, 0, -1 }, { -1, 0, -1 },
                                     { 0, 1, 1 }, { 0, -1, 1 }, { 0, 1, -1 }, { 0, -1, -1 } };
    private static int grad4[][] = { { 0, 1, 1, 1 }, { 0, 1, 1, -1 }, { 0, 1, -1, 1 }, { 0, 1, -1, -1 },
                                     { 0, -1, 1, 1 }, { 0, -1, 1, -1 }, { 0, -1, -1, 1 }, { 0, -1, -1, -1 },
                                     { 1, 0, 1, 1 }, { 1, 0, 1, -1 }, { 1, 0, -1, 1 }, { 1, 0, -1, -1 },
                                     { -1, 0, 1, 1 }, { -1, 0, 1, -1 }, { -1, 0, -1, 1 }, { -1, 0, -1, -1 },
                                     { 1, 1, 0, 1 }, { 1, 1, 0, -1 }, { 1, -1, 0, 1 }, { 1, -1, 0, -1 },
                                     { -1, 1, 0, 1 }, { -1, 1, 0, -1 }, { -1, -1, 0, 1 }, { -1, -1, 0, -1 },
                                     { 1, 1, 1, 0 }, { 1, 1, -1, 0 }, { 1, -1, 1, 0 }, { 1, -1, -1, 0 },
                                     { -1, 1, 1, 0 }, { -1, 1, -1, 0 }, { -1, -1, 1, 0 }, { -1, -1, -1, 0 } };
    private static int p[] = { 151, 160, 137, 91, 90, 15,
                               131, 13, 201, 95, 96, 53, 194, 233, 7, 225, 140, 36, 103, 30, 69, 142, 8, 99, 37, 240, 21, 10, 23,
                               190, 6, 148, 247, 120, 234, 75, 0, 26, 197, 62, 94, 252, 219, 203, 117, 35, 11, 32, 57, 177, 33,
                               88, 237, 149, 56, 87, 174, 20, 125, 136, 171, 168, 68, 175, 74, 165, 71, 134, 139, 48, 27, 166,
                               77, 146, 158, 231, 83, 111, 229, 122, 60, 211, 133, 230, 220, 105, 92, 41, 55, 46, 245, 40, 244,
                               102, 143, 54, 65, 25, 63, 161, 1, 216, 80, 73, 209, 76, 132, 187, 208, 89, 18, 169, 200, 196,
                               135, 130, 116, 188, 159, 86, 164, 100, 109, 198, 173, 186, 3, 64, 52, 217, 226, 250, 124, 123,
                               5, 202, 38, 147, 118, 126, 255, 82, 85, 212, 207, 206, 59, 227, 47, 16, 58, 17, 182, 189, 28, 42,
                               223, 183, 170, 213, 119, 248, 152, 2, 44, 154, 163, 70, 221, 153, 101, 155, 167, 43, 172, 9,
                               129, 22, 39, 253, 19, 98, 108, 110, 79, 113, 224, 232, 178, 185, 112, 104, 218, 246, 97, 228,
                               251, 34, 242, 193, 238, 210, 144, 12, 191, 179, 162, 241, 81, 51, 145, 235, 249, 14, 239, 107,
                               49, 192, 214, 31, 181, 199, 106, 157, 184, 84, 204, 176, 115, 121, 50, 45, 127, 4, 150, 254,
                               138, 236, 205, 93, 222, 114, 67, 29, 24, 72, 243, 141, 128, 195, 78, 66, 215, 61, 156, 180 };
    // To remove the need for index wrapping, double the permutation table length
    private static int perm[] = new int[512];

    static
    {
        for ( int i = 0; i < 512; i++ )
        {
            perm[ i ] = p[ i & 255 ];
        }
    }
    // A lookup table to traverse the simplex around a given point in 4D.
    // Details can be found where this table is used, in the 4D noise method.
    private static int simplex[][] = {
            { 0, 1, 2, 3 }, { 0, 1, 3, 2 }, { 0, 0, 0, 0 }, { 0, 2, 3, 1 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 1, 2, 3, 0 },
            { 0, 2, 1, 3 }, { 0, 0, 0, 0 }, { 0, 3, 1, 2 }, { 0, 3, 2, 1 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 1, 3, 2, 0 },
            { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 },
            { 1, 2, 0, 3 }, { 0, 0, 0, 0 }, { 1, 3, 0, 2 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 2, 3, 0, 1 }, { 2, 3, 1, 0 },
            { 1, 0, 2, 3 }, { 1, 0, 3, 2 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 2, 0, 3, 1 }, { 0, 0, 0, 0 }, { 2, 1, 3, 0 },
            { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 },
            { 2, 0, 1, 3 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 3, 0, 1, 2 }, { 3, 0, 2, 1 }, { 0, 0, 0, 0 }, { 3, 1, 2, 0 },
            { 2, 1, 0, 3 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 0, 0, 0, 0 }, { 3, 1, 0, 2 }, { 0, 0, 0, 0 }, { 3, 2, 0, 1 }, { 3, 2, 1, 0 } };
    // This method is a *lot* faster than using (int)Math.floor(x)

    private static int fastfloor( double x )
    {
        return x > 0 ? (int) x : (int) x - 1;
    }

    private static double dot( int g[], double x, double y )
    {
        return g[ 0 ] * x + g[ 1 ] * y;
    }

    private static double dot( int g[], double x, double y, double z )
    {
        return g[ 0 ] * x + g[ 1 ] * y + g[ 2 ] * z;
    }

    private static double dot( int g[], double x, double y, double z, double w )
    {
        return g[ 0 ] * x + g[ 1 ] * y + g[ 2 ] * z + g[ 3 ] * w;
    }

    /**
     * 1D simplex noise
     */
    public static double noise( double xin ) {
        // TODO: Implement actual fast 1 D noise
        // For now, use 2D noise with fixed axis
        return noise(xin, 12543.213);
    }

    /**
     * 2D simplex noise
     */
    public static double noise( double xin, double yin )
    {
        double n0, n1, n2; // Noise contributions from the three corners
        // Skew the input space to determine which simplex cell we're in
        final double F2 = 0.5 * ( Math.sqrt( 3.0 ) - 1.0 );
        double s = ( xin + yin ) * F2; // Hairy factor for 2D
        int i = fastfloor( xin + s );
        int j = fastfloor( yin + s );
        final double G2 = ( 3.0 - Math.sqrt( 3.0 ) ) / 6.0;
        double t = ( i + j ) * G2;
        double X0 = i - t; // Unskew the cell origin back to (x,y) space
        double Y0 = j - t;
        double x0 = xin - X0; // The x,y distances from the cell origin
        double y0 = yin - Y0;
        // For the 2D case, the simplex shape is an equilateral triangle.
        // Determine which simplex we are in.
        int i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords
        if ( x0 > y0 )
        {
            i1 = 1;
            j1 = 0;
        } // lower triangle, XY order: (0,0)->(1,0)->(1,1)
        else
        {
            i1 = 0;
            j1 = 1;
        }         // upper triangle, YX order: (0,0)->(0,1)->(1,1)
        // A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and
        // a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
        // c = (3-sqrt(3))/6
        double x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
        double y1 = y0 - j1 + G2;
        double x2 = x0 - 1.0 + 2.0 * G2; // Offsets for last corner in (x,y) unskewed coords
        double y2 = y0 - 1.0 + 2.0 * G2;
        // Work out the hashed gradient indices of the three simplex corners
        int ii = i & 255;
        int jj = j & 255;
        int gi0 = perm[ ii + perm[ jj ] ] % 12;
        int gi1 = perm[ ii + i1 + perm[ jj + j1 ] ] % 12;
        int gi2 = perm[ ii + 1 + perm[ jj + 1 ] ] % 12;
        // Calculate the contribution from the three corners
        double t0 = 0.5 - x0 * x0 - y0 * y0;
        if ( t0 < 0 )
        {
            n0 = 0.0;
        }
        else
        {
            t0 *= t0;
            n0 = t0 * t0 * dot( grad3[ gi0 ], x0, y0 ); // (x,y) of grad3 used for 2D gradient
        }
        double t1 = 0.5 - x1 * x1 - y1 * y1;
        if ( t1 < 0 )
        {
            n1 = 0.0;
        }
        else
        {
            t1 *= t1;
            n1 = t1 * t1 * dot( grad3[ gi1 ], x1, y1 );
        }
        double t2 = 0.5 - x2 * x2 - y2 * y2;
        if ( t2 < 0 )
        {
            n2 = 0.0;
        }
        else
        {
            t2 *= t2;
            n2 = t2 * t2 * dot( grad3[ gi2 ], x2, y2 );
        }
        // Add contributions from each corner to get the final noise value.
        // The result is scaled to return values in the interval [-1,1].
        return 70.0 * ( n0 + n1 + n2 );
    }

    /**
     * 3D simplex noise
     */
    public static double noise( double xin, double yin, double zin )
    {
        double n0, n1, n2, n3; // Noise contributions from the four corners
        // Skew the input space to determine which simplex cell we're in
        final double F3 = 1.0 / 3.0;
        double s = ( xin + yin + zin ) * F3; // Very nice and simple skew factor for 3D
        int i = fastfloor( xin + s );
        int j = fastfloor( yin + s );
        int k = fastfloor( zin + s );
        final double G3 = 1.0 / 6.0; // Very nice and simple unskew factor, too
        double t = ( i + j + k ) * G3;
        double X0 = i - t; // Unskew the cell origin back to (x,y,z) space
        double Y0 = j - t;
        double Z0 = k - t;
        double x0 = xin - X0; // The x,y,z distances from the cell origin
        double y0 = yin - Y0;
        double z0 = zin - Z0;
        // For the 3D case, the simplex shape is a slightly irregular tetrahedron.
        // Determine which simplex we are in.
        int i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords
        int i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords
        if ( x0 >= y0 )
        {
            if ( y0 >= z0 )
            {
                i1 = 1;
                j1 = 0;
                k1 = 0;
                i2 = 1;
                j2 = 1;
                k2 = 0;
            } // X Y Z order
            else if ( x0 >= z0 )
            {
                i1 = 1;
                j1 = 0;
                k1 = 0;
                i2 = 1;
                j2 = 0;
                k2 = 1;
            } // X Z Y order
            else
            {
                i1 = 0;
                j1 = 0;
                k1 = 1;
                i2 = 1;
                j2 = 0;
                k2 = 1;
            } // Z X Y order
        }
        else
        { // x0<y0
            if ( y0 < z0 )
            {
                i1 = 0;
                j1 = 0;
                k1 = 1;
                i2 = 0;
                j2 = 1;
                k2 = 1;
            } // Z Y X order
            else if ( x0 < z0 )
            {
                i1 = 0;
                j1 = 1;
                k1 = 0;
                i2 = 0;
                j2 = 1;
                k2 = 1;
            } // Y Z X order
            else
            {
                i1 = 0;
                j1 = 1;
                k1 = 0;
                i2 = 1;
                j2 = 1;
                k2 = 0;
            } // Y X Z order
        }
        //  A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z),
        //  a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and
        //  a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where
        //  c = 1/6.
        double x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
        double y1 = y0 - j1 + G3;
        double z1 = z0 - k1 + G3;
        double x2 = x0 - i2 + 2.0 * G3; // Offsets for third corner in (x,y,z) coords
        double y2 = y0 - j2 + 2.0 * G3;
        double z2 = z0 - k2 + 2.0 * G3;
        double x3 = x0 - 1.0 + 3.0 * G3; // Offsets for last corner in (x,y,z) coords
        double y3 = y0 - 1.0 + 3.0 * G3;
        double z3 = z0 - 1.0 + 3.0 * G3;
        // Work out the hashed gradient indices of the four simplex corners
        int ii = i & 255;
        int jj = j & 255;
        int kk = k & 255;
        int gi0 = perm[ ii + perm[ jj + perm[ kk ] ] ] % 12;
        int gi1 = perm[ ii + i1 + perm[ jj + j1 + perm[ kk + k1 ] ] ] % 12;
        int gi2 = perm[ ii + i2 + perm[ jj + j2 + perm[ kk + k2 ] ] ] % 12;
        int gi3 = perm[ ii + 1 + perm[ jj + 1 + perm[ kk + 1 ] ] ] % 12;
        // Calculate the contribution from the four corners
        double t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0;
        if ( t0 < 0 )
        {
            n0 = 0.0;
        }
        else
        {
            t0 *= t0;
            n0 = t0 * t0 * dot( grad3[ gi0 ], x0, y0, z0 );
        }
        double t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1;
        if ( t1 < 0 )
        {
            n1 = 0.0;
        }
        else
        {
            t1 *= t1;
            n1 = t1 * t1 * dot( grad3[ gi1 ], x1, y1, z1 );
        }
        double t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2;
        if ( t2 < 0 )
        {
            n2 = 0.0;
        }
        else
        {
            t2 *= t2;
            n2 = t2 * t2 * dot( grad3[ gi2 ], x2, y2, z2 );
        }
        double t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3;
        if ( t3 < 0 )
        {
            n3 = 0.0;
        }
        else
        {
            t3 *= t3;
            n3 = t3 * t3 * dot( grad3[ gi3 ], x3, y3, z3 );
        }
        // Add contributions from each corner to get the final noise value.
        // The result is scaled to stay just inside [-1,1]
        return 32.0 * ( n0 + n1 + n2 + n3 );
    }

    /**
     * 4D simplex noise
     */
    public static double noise( double x, double y, double z, double w )
    {
        // The skewing and unskewing factors are hairy again for the 4D case
        final double F4 = ( Math.sqrt( 5.0 ) - 1.0 ) / 4.0;
        final double G4 = ( 5.0 - Math.sqrt( 5.0 ) ) / 20.0;
        double n0, n1, n2, n3, n4; // Noise contributions from the five corners
        // Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in
        double s = ( x + y + z + w ) * F4; // Factor for 4D skewing
        int i = fastfloor( x + s );
        int j = fastfloor( y + s );
        int k = fastfloor( z + s );
        int l = fastfloor( w + s );
        double t = ( i + j + k + l ) * G4; // Factor for 4D unskewing
        double X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
        double Y0 = j - t;
        double Z0 = k - t;
        double W0 = l - t;
        double x0 = x - X0; // The x,y,z,w distances from the cell origin
        double y0 = y - Y0;
        double z0 = z - Z0;
        double w0 = w - W0;
        // For the 4D case, the simplex is a 4D shape I won't even try to describe.
        // To find out which of the 24 possible simplices we're in, we need to
        // determine the magnitude ordering of x0, y0, z0 and w0.
        // The method below is a good way of finding the ordering of x,y,z,w and
        // then find the correct traversal order for the simplex we’re in.
        // First, six pair-wise comparisons are performed between each possible pair
        // of the four coordinates, and the results are used to add up binary bits
        // for an integer index.
        int c1 = ( x0 > y0 ) ? 32 : 0;
        int c2 = ( x0 > z0 ) ? 16 : 0;
        int c3 = ( y0 > z0 ) ? 8 : 0;
        int c4 = ( x0 > w0 ) ? 4 : 0;
        int c5 = ( y0 > w0 ) ? 2 : 0;
        int c6 = ( z0 > w0 ) ? 1 : 0;
        int c = c1 + c2 + c3 + c4 + c5 + c6;
        int i1, j1, k1, l1; // The integer offsets for the second simplex corner
        int i2, j2, k2, l2; // The integer offsets for the third simplex corner
        int i3, j3, k3, l3; // The integer offsets for the fourth simplex corner
        // simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order.
        // Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w and x<w
        // impossible. Only the 24 indices which have non-zero entries make any sense.
        // We use a thresholding to set the coordinates in turn from the largest magnitude.
        // The number 3 in the "simplex" array is at the position of the largest coordinate.
        i1 = simplex[ c ][ 0 ] >= 3 ? 1 : 0;
        j1 = simplex[ c ][ 1 ] >= 3 ? 1 : 0;
        k1 = simplex[ c ][ 2 ] >= 3 ? 1 : 0;
        l1 = simplex[ c ][ 3 ] >= 3 ? 1 : 0;
        // The number 2 in the "simplex" array is at the second largest coordinate.
        i2 = simplex[ c ][ 0 ] >= 2 ? 1 : 0;
        j2 = simplex[ c ][ 1 ] >= 2 ? 1 : 0;
        k2 = simplex[ c ][ 2 ] >= 2 ? 1 : 0;
        l2 = simplex[ c ][ 3 ] >= 2 ? 1 : 0;
        // The number 1 in the "simplex" array is at the second smallest coordinate.
        i3 = simplex[ c ][ 0 ] >= 1 ? 1 : 0;
        j3 = simplex[ c ][ 1 ] >= 1 ? 1 : 0;
        k3 = simplex[ c ][ 2 ] >= 1 ? 1 : 0;
        l3 = simplex[ c ][ 3 ] >= 1 ? 1 : 0;
        // The fifth corner has all coordinate offsets = 1, so no need to look that up.
        double x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
        double y1 = y0 - j1 + G4;
        double z1 = z0 - k1 + G4;
        double w1 = w0 - l1 + G4;
        double x2 = x0 - i2 + 2.0 * G4; // Offsets for third corner in (x,y,z,w) coords
        double y2 = y0 - j2 + 2.0 * G4;
        double z2 = z0 - k2 + 2.0 * G4;
        double w2 = w0 - l2 + 2.0 * G4;
        double x3 = x0 - i3 + 3.0 * G4; // Offsets for fourth corner in (x,y,z,w) coords
        double y3 = y0 - j3 + 3.0 * G4;
        double z3 = z0 - k3 + 3.0 * G4;
        double w3 = w0 - l3 + 3.0 * G4;
        double x4 = x0 - 1.0 + 4.0 * G4; // Offsets for last corner in (x,y,z,w) coords
        double y4 = y0 - 1.0 + 4.0 * G4;
        double z4 = z0 - 1.0 + 4.0 * G4;
        double w4 = w0 - 1.0 + 4.0 * G4;
        // Work out the hashed gradient indices of the five simplex corners
        int ii = i & 255;
        int jj = j & 255;
        int kk = k & 255;
        int ll = l & 255;
        int gi0 = perm[ ii + perm[ jj + perm[ kk + perm[ ll ] ] ] ] % 32;
        int gi1 = perm[ ii + i1 + perm[ jj + j1 + perm[ kk + k1 + perm[ ll + l1 ] ] ] ] % 32;
        int gi2 = perm[ ii + i2 + perm[ jj + j2 + perm[ kk + k2 + perm[ ll + l2 ] ] ] ] % 32;
        int gi3 = perm[ ii + i3 + perm[ jj + j3 + perm[ kk + k3 + perm[ ll + l3 ] ] ] ] % 32;
        int gi4 = perm[ ii + 1 + perm[ jj + 1 + perm[ kk + 1 + perm[ ll + 1 ] ] ] ] % 32;
        // Calculate the contribution from the five corners
        double t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0;
        if ( t0 < 0 )
        {
            n0 = 0.0;
        }
        else
        {
            t0 *= t0;
            n0 = t0 * t0 * dot( grad4[ gi0 ], x0, y0, z0, w0 );
        }
        double t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1;
        if ( t1 < 0 )
        {
            n1 = 0.0;
        }
        else
        {
            t1 *= t1;
            n1 = t1 * t1 * dot( grad4[ gi1 ], x1, y1, z1, w1 );
        }
        double t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2;
        if ( t2 < 0 )
        {
            n2 = 0.0;
        }
        else
        {
            t2 *= t2;
            n2 = t2 * t2 * dot( grad4[ gi2 ], x2, y2, z2, w2 );
        }
        double t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3;
        if ( t3 < 0 )
        {
            n3 = 0.0;
        }
        else
        {
            t3 *= t3;
            n3 = t3 * t3 * dot( grad4[ gi3 ], x3, y3, z3, w3 );
        }
        double t4 = 0.6 - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4;
        if ( t4 < 0 )
        {
            n4 = 0.0;
        }
        else
        {
            t4 *= t4;
            n4 = t4 * t4 * dot( grad4[ gi4 ], x4, y4, z4, w4 );
        }
        // Sum up and scale the result to cover the range [-1,1]
        return 27.0 * ( n0 + n1 + n2 + n3 + n4 );
    }
}

